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BACKGROUND: the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). When baseline contributions occur in the data, the background profile retrieved with MCR-ALS may show abnormal lumps or negative dips at the position of the remaining component peaks. RESULTS: The phenomenon is shown to be due to remaining rotational ambiguity in the obtained profiles, as confirmed by the estimation of the boundaries of the range of feasible bilinear profiles. To avoid the abnormal features in the retrieved profile, a new background interpolation constraint is proposed and described in detail. Both simulated and experimental data are employed to support the need of the new MCR-ALS constraint. In the latter case, the estimated analyte concentrations agreed with those previously reported. SIGNIFICANCE: The developed procedure helps to reduce the extent of rotational ambiguity in the solution and to better interpret the results on physicochemical grounds.

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Parallel factor analysis 2 (PARAFAC2) is still being advocated for the processing of second-order chromatographic-spectral data, both for qualitative and quantitative applications. However, neither classical PARAFAC2 nor the newly developed flexible non-negative NN-PARAFAC2 version can adequately model these data in a general situation. In quantitative analysis, considerable bias may result in the estimation of analyte concentrations, due to the fact that both PARAFAC2 models apply an artificial constraint to the retrieved profiles, requiring constant cross-product, i.e., constant overlapping, between all pairs of component elution profiles in all samples. This only occurs under limited conditions. In this report, simulations help to understand, visualize and interpret these PARAFAC2 features. Experimental data are also studied concerning the determination of a fluoroquinolone antibiotic in bovine liver samples by liquid chromatography with multi-wavelength fluorescence detection. Both for simulated and experimental data, the PARAFAC2 versions provide poor analytical results, while correct data processing and reasonable analytical indicators can be achieved using multivariate curve resolution - alternating least-squares (MCR-ALS). For the simulated data sets, root mean square errors/relative errors of prediction were 0.01 concentration units/2% for MCR-ALS, compared to 0.02-0.06 units/4-12% for both PARAFAC2 and NN-PARAFAC2. For the experimental data sets, they were 0.025 µg mL-1/11% for MCR-ALS, 0.09 µg mL-1/40% for PARAFAC2 and 0.16 µg mL-1/71% for NN-PARAFAC2, with average recoveries (standard deviation) of 91(14)%, 185(135)% and 69(35)% respectively.

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The endocrine disrupting chemicals bisphenol A (BPA) and 4-nonylphenol (NP) were simultaneously quantified through third-order/four-way calibration. Excitation-emission fluorescence matrix-kinetic (EEFM-K) third-order data were generated by measuring the EEFMs of these priority xenoestrogens as a function of reaction time during their Fenton degradation. Third-order/four-way calibration notably improves the sensitivity of the method and provides the required selectivity for quantifying analytes with critically overlapped fluorescence signals. In fact, collinearity between BPA and NP emission spectra prevented their quantification using EEFM second-order data and three-way PARAFAC (parallel factor analysis); however, the addition of a third instrumental mode allowed the correct chemometric modeling with four-way PARAFAC. In this way, the compliance of Kruskal's theorem extended to higher-order data was verified. The method was applied for the determination of the analytes in samples of different plastic materials, which are in contact with food and/or beverages. In these cases, where unmodelled constituents are present, good results for BPA were achieved with four-way PARAFAC, but the predictions for NP using this model were deficient. A better predictive capability for NP in real samples was achieved when either U-PLS/RTL (unfolded partial least-squares combined with residual trilinearization) or MCR-ALS (multivariate curve resolution with alternating least-squares) was applied for data processing, demonstrating the power of these latter models for the resolution of more complex systems.

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For the first time, a third-order/four-way system having instrumental modes depending on each other was experimentally generated and it was successfully resolved. Non-quadrilinear type 4 data, constituted by liquid chromatographic elution times (LC) and excitation-emission fluorescence matrices (EEFMs), were on-line measured using conventional equipment. Thus, third-order/four-way data, valuable for giving rise to highly sensitive and selective methods, were obtained minimizing significantly the experimental work and time, in comparison with the reported strategies for the acquisition of LC-EEFM data. The usefulness of MCR-ALS (multivariate curve resolution-alternating least square) for attaining reliable results from data with two mutually dependent instrumental modes, namely elution time and excitation wavelength modes, was established through the simultaneous quantitation of benz[a]anthracene, chrysene, benzo[b]fluoranthene, and benzo[a]pyrene. Limits of detection in the range 1.0-1.4 ng mL-1 were achieved for the target polycyclic aromatic hydrocarbons, allowing their determination in about 9 min per sample in leaves of different types of tea.

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For the first time, third-order liquid chromatography with excitation-emission fluorescence matrix detection (LC-EEFM) data were generated on-line and chemometrically processed for the simultaneous quantitation of the heavy-polycyclic aromatic hydrocarbons fluoranthene, pyrene, benz[a]anthracene, chrysene, benzo[b]fluoranthene, benzo[k]fluoranthene, benzo[a]pyrene, and dibenz[a,h]anthracene. The applied experimental strategy is very simple, and is based on the reduction of the linear flow rate by fitting a larger diameter connecting-tube between the column outlet and the fluorimetric detector. In this way, EEFMs were successfully recorded on-line, without involving a large total analysis time. Because in the studied system quadrilinearity was fulfilled, four-way parallel factor (PARAFAC) analysis was applied for data processing. The second-order advantage, which is an intrinsic property of data of at least second-order, allowed the quantification of the analytes in interfering media. Moreover, resolution of the system with a high degree of collinearity was achieved thanks to the third-order advantage. In addition to a selectivity improvement, third-order/four-way calibration increased the sensitivity, with limits of detection in the range of 0.4-2.9ngmL-1. After a solid-phase extraction procedure with C18 membranes, considerably lower concentrations (between 0.033-2.70ngmL-1) were determined in real waters, with most recoveries in the range 90-106%.

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In this work, the combination of chemometric techniques with kinetic-spectroscopic data allowed quantifying two dyes (tartrazine and carminic acid) in complex matrices as mustard, ketchup, asparagus soup powder, pumpkin soup powder, plum jam and orange-strawberry juice. Quantitative analysis was performed without the use of tedious sample pretreatment, due to the achievement of the second-order advantage. The results obtained showed an improvement in simplicity, speed and cost with respect to usual separation techniques, allowing to properly quantifying these dyes obtaining limits of detection below 0.6mgL-1. In addition, to the best of our knowledge, is the first time that kinetic-spectroscopic data are obtained from the action of laccase for analytical purposes.

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For the first time, a simple and environmentally friendly third-order/four-way calibration was applied for the simultaneous determination of five heavy-polycyclic aromatic hydrocarbons (PAHs) in interfering environments. The kinetic evolution of the Fenton degradation of benzo[a]pyrene, dibenz[a,h]anthracene, benzo[b]fluoranthene, benzo[k]fluoranthene and benz[a]anthracene was followed by recording full excitation-emission fluorescence matrices (EEFMs) of the samples at different reaction times, obtaining third-order EEFM-kinetic (EEFM-K) data. The sensitivity of the method was increased by carrying out the reaction in the presence of methyl-ß-cyclodextrin. The four-way parallel factor (PARAFAC) algorithm, which was used for data processing, exploits the second-order advantage, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. The clear superiority of the applied approach in comparison with second-order/three-way calibration performed with unreacting EEFMs is demonstrated, using two sets of samples with foreign compounds with particular spectral profiles. In one of the latter sets, the existence of a third-order advantage was explored and discussed. The feasibility to directly determine parts-per-trillion concentration levels of PAHs after a very simple solid-phase extraction with C18 membranes is established with natural water samples containing uncalibrated constituents.

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Valuable quantitative information could be obtained from strongly overlapped chromatographic profiles of two enantiomers by using proper chemometric methods. Complete separation profiles where the peaks are fully resolved are difficult to achieve in chiral separation methods, and this becomes a particularly severe problem in case that the analyst needs to measure the chiral purity, i.e., when one of the enantiomers is present in the sample in very low concentrations. In this report, we explore the scope of a multivariate chemometric technique based on unfolded partial least-squares regression, as a mathematical tool to solve this quite frequent difficulty. This technique was applied to obtain quantitative results from partially overlapped chromatographic profiles of R- and S-ketoprofen, with different values of enantioresolution factors (from 0.81 down to less than 0.2 resolution units), and also at several different S:R enantiomeric ratios. Enantiomeric purity below 1% was determined with excellent precision even from almost completely overlapped signals. All these assays were tested on the most demanding condition, i.e., when the minor peak elutes immediately after the main peak. The results were validated using univariate calibration of completely resolved profiles and the method applied to the determination of enantiomeric purity of commercial pharmaceuticals.

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This report reviews recent literature on the application of multivariate calibration techniques to both first- and second-order data, aimed at the analytical determination of analytes of interest or sample properties in a variety of industrial, pharmaceutical, food, and environmental samples, including examples of process control. The most used data processing tools are briefly described, with emphasis on the advantages that can be obtained by applying specific combinations of multivariate data and algorithms. The main focus is on works devoted to first-order data (i.e., spectra, chromatograms, etc.) combined with partial least-squares regression, which has become the standard for this type of analytical research. A brief discussion on recent work on second-order data and algorithms is also included, as this field is rapidly growing, although at present it does not show, the general applicability of the first-order counterparts.

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The aim of this work was to quantify five commonly used pesticides (propoxur, carbaryl, carbendazim, thiabendazole and fuberidazole) in real samples as: tomato, orange juice, grapefruit juice, lemon and tangerine. The method used for the determination of these analytes in the complex matrices was high-performance liquid chromatography with diode array detection. In order to work under isocratic conditions and to complete each run in less than 10 min, the analysis was carried out applying multivariate curve resolution coupled to alternating least-squares (MCR-ALS). The flexibility of this applied multivariate model allowed the prediction of the concentrations of the five analytes in complex samples including strongly coeluting analytes, elution time shifts, band shape changes and presence of uncalibrated interferents. The obtained limits of detection (in µg L(-1)) using the proposed methodology were 2.3 (carbendazim), 0.90 (thiabendazole), 12 (propoxur), 0.46 (fuberidazole) and 0.32 (carbaryl).

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In this report, we demonstrate how chiral liquid chromatography combined with multivariate chemometric techniques, specifically unfolded-partial least-squares regression (U-PLS), provides a powerful analytical methodology. Using U-PLS, strongly overlapped enantiomer profiles in a sample could be successfully processed and enantiomeric purity could be accurately determined without requiring baseline enantioresolution between peaks. The samples were partially enantioseparated with a permethyl-ß-cyclodextrin chiral column under reversed-phase conditions. Signals detected with a diode-array detector within a wavelength range from 198 to 241 nm were recorded, and the data were processed by a second-order multivariate algorithm to decrease detection limits. The R-(-)-enantiomer of ibuprofen in tablet formulation samples could be determined at the level of 0.5 mg L⁻¹ in the presence of 99.9% of the S-(+)-enantiomorph with relative prediction error within ±3%.

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Quantitative analytical works developed by processing second- and third-order chromatographic data are reviewed. The various modes in which data of complex structure can be measured are discussed, with chromatographic separation providing either one or two of the data dimensions. This produces second-order data (matrices from uni-dimensional chromatography with multivariate detection or from two-dimensional chromatography) or third-order data (three-dimensional data arrays from two-dimensional chromatography with multivariate detection). The available algorithms for processing these data are classified and discussed, regarding their ability to cope with the ubiquitous phenomenon of retention time shifts from run to run. A summary of relevant works applying this combination of techniques is presented, with focus on quantitative analytical results. Special attention is paid to works achieving the full potentiality of the multidimensional data, i.e., the second-order advantage.

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The most concerned polycyclic aromatic hydrocarbons (PAHs) benzo[a]pyrene, dibenz[a,h]anthracene, chrysene, benzo[b]fluoranthene, benzo[k]fluoranthene and benz[a]anthracene were simultaneously determined in the presence of other 10 interfering PAHs, applying second-order multivariate calibration to the data obtained with a flow-through optosensor interfaced to a fast-scanning spectrofluorimeter. Using a sample volume of 2.5 mL, detection limits in the range 5-115 ng L(-1) were obtained in interfering samples, with a sample frequency of ca. 15 samples per hour, and with a minimum use of organic solvents, competing very favorably with chromatographic methods. The significance of this study lies in the solution of the quantitative analysis problem of six PAHs in real matrices of unknown composition. The unfolded partial least-squares/residual bilinearization (U-PLS/RBL) algorithm showed the best performance in resolving the complex studied system.

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Multivariate calibration coupled to high-performance liquid chromatography-fast scanning fluorescence spectroscopy (HPLC-FSFS) was employed for the analysis of 10 selected polycyclic aromatic hydrocarbons (PAHs), six of which correspond to heavy PAHs. The goal of the present study was the successful resolution of a system even in the presence of real interferences. Second-order HPLC-FSFS data matrices were obtained in a short time with a chromatographic system operating in isocratic mode. The difficulties in aligning chromatographic bands in complex systems, such as the ones presented here, are discussed. Two second-order calibration algorithms which do not require chromatographic alignment were selected for data processing, namely, multivariate curve resolution-alternating least-squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2). These algorithms did also achieve the second-order advantage, and therefore they were able to overcome the problem of the presence of unexpected interferences. The study was employed for the discussion of the scopes of the applied second-order chemometric tools, demonstrating the superiority of MCR-ALS to successfully resolve this complex system. The quality of the proposed techniques was assessed on the basis of the analytical recoveries from different types of water and olive oil samples after solid-phase extraction. The studied concentration ranges in water samples were 5.6 x 10(-3)-0.20 ng mL(-1) for heavy PAHs and 0.036-0.80 ng mL(-1) for light PAHs, while in oil samples the PAHs concentrations were 0.13-9.6 and 2.3-49.5 ng mL(-1) for heavy and light PAHS, respectively. All real samples were analyzed in the presence of the studied interferences.

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This work presents a novel approach for the simultaneous ultratrace determination of benzo[ a]pyrene and dibenzo[ a,h]anthracene, the two most carcinogenic polycyclic aromatic hydrocarbons (PAHs), in a very interfering environment, combining the recently discovered ability of the nylon membrane to strongly retain and concentrate PAHs on its surface, the sensitivity of molecular fluorescence, and the selectivity of second-order chemometric algorithms. The fluorescence excitation-emission matrices, directly measured on a nylon-membrane surface, are processed by applying parallel factor analysis (PARAFAC) and unfolded partial least-squares coupled to residual bilinearization (U-PLS/RBL). The superiority of U-PLS/RBL to quantify BaP and DBA at concentrations below 10 ng L (-1) in the presence of the remaining 14 US EPA (United States Environmental Protection Agency) PAHs at total concentrations ranging from 1400 and 14,000 ng L (-1) is demonstrated. The present method successfully faces this complex challenge without using organic solvents, which are to known produce environmental contamination. Finally, the high sensitivity of the present method avoids preconcentration and elution steps, considerably decreasing the analysis time and the experimental errors. Because the instrumental involved in the determination is nonsophisticated, the experiments could be carried out in routine laboratories.

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Room-temperature phosphorescence excitation-emission matrices and multiway methods have been analyzed as potential tools for screening oil samples, based on full matrix information for polyaromatic hydrocarbons. Crude oils obtained from different sources of similar geographic origin, as well as light and heavy lubricating oils, were analyzed. The room-temperature phosphorescence matrix signals were processed by applying multilayer perceptron artificial neural networks, parallel factor analysis coupled to linear discriminant analysis, discriminant unfolded partial least-squares, and discriminant multidimensional partial least-squares (DN-PLS). The ability of the latter algorithm to classify the investigated oils into four categories is demonstrated. In addition, the combination of DN-PLS with residual bilinearization allows for a proper classification of oils containing unsuspected compounds not present in the training sample set. This second-order advantage concept is applied to a classification study for the first time. The employed approach is fast, avoids the use of laborious chromatographic analysis, and is relevant for oil characterization, identification, and determination of accidental spill sources.

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The present article describes the simultaneous phosphorimetric determination of pyrene and benzo[a]pyrene, two highly toxic polycyclic aromatic hydrocarbons, through excitation-emission phosphorescence matrices (EEPMs) and second-order calibration. The developed approach enabled us to determine both compounds at microg L(-1) concentration levels without the necessity of applying separation steps, as well as significantly reducing the experimental time. An artificial neural network (ANN) approach was applied to optimize the chemical variables which have an influence on the room-temperature phosphorescence emission of the studied analytes. The present study was employed for the discussion of the scopes of the applied second-order chemometric tools: parallel factor analysis (PARAFAC) and partial least-squares with residual bilinearization (PLS/RBL). The superior capability of PLS/RBL to model the profiles of other potentially interferent polycyclic aromatic hydrocarbons (PAHs) was demonstrated. The quality of the proposed method was established with the determination of both pyrene and benzo[a]pyrene in artificial and real water samples.

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A second-order multivariate calibration approach, based on a combination of unfolded-partial least-squares with residual bilinearization (U-PLS/RBL), has been applied to fluorescence excitation-emission matrix data for multicomponent mixtures showing inner filter effects. The employed chemometric algorithm is the most successful one regarding the prediction of analyte concentrations when significant inner filter effects occur, even in the presence of unexpected sample components, which require strict adherence to the second-order advantage. Results for simulated fluorescence excitation-emission data are described, in comparison with the classical approach based on parallel factor analysis and other second-order algorithms, including generalized rank annihilation, bilinear least squares combined with residual bilinearization and multivariate curve resolution-alternating leastsquares. A set of experimental data was also studied, in which calibration was performed with fluorescence excitation-emission matrices for samples containing mixtures of chrysene (the analyte of interest) and benzopyrene (which produced strong inner filter effect across the useful wavelength range). Prediction was made on validation samples with a qualitative composition similar to the calibration set, and also on test samples containing an unexpected component (pyrene). In this latter case, U-PLS/RBL showed a unique success for the analysis of the calibrated component chrysene, achieving the useful second-order advantage.

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Four-way fluorescence data recorded by following the kinetic evolution of excitation-emission fluorescence matrices (EEMs) have been analyzed by parallel factor analysis and trilinear least-squares algorithms. These methodologies exploit the second-order advantage of the studied data, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. They were applied to the simultaneous determination of the components of the anticancer combination of methotrexate and leucovorin in human urine samples. Both analytes were converted into highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics of the reaction was continuously monitored by recording full EEM of the samples at different reaction times. A commercial fast scanning spectrofluorometer has been used for the first time to measure the four-way EEM kinetic data. The rapid scanning instrument allows the acquisition of a complete EEM in 12 s at a wavelength scanning speed of 24 000 nm/min. The emission spectra were recorded from 335 to 490 nm at 5-nm intervals, exciting from 255 to 315 nm at 6-nm intervals. Ten successive EEMs were measured at 72-s intervals, to follow the fluorescence kinetic evolution of the mixture components. Good recoveries were obtained in synthetic binary samples and also in spiked urine samples. The excitation, emission, and kinetic time profiles recovered by both chemometric techniques are in good agreement with experimental observations.

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First- and second-order multivariate calibration of fluorescence data have been compared as regards the determination of anti-inflammatories and metabolites in the biological fluids serum and urine. The simultaneous resolution of naproxen-salicylic acid mixtures in serum and naproxen-salicylic acid-salicyluric acid mixtures in urine was accomplished and employed for a discussion of the relative advantages of the applied chemometric tools. The analysis of second-order fluorescence excitation-emission matrices was performed using iteratively reweighted generalized rank annihilation method (IRGRAM), parallel factor analysis (PARAFAC), and self-weighted alternating trilinear decomposition (SWATLD). The results were compared with first-order fluorescence emission data analyzed with partial least-squares regression (PLS). In all cases, the performance of the methods was improved through the formation of inclusion complexes of the analytes with beta-cyclodextrin. The concentration ranges in which the analytes could be determined were as follows: naproxen, 0-250 ng mL(-1) in serum and 0-200 ng mL(-1) in urine; salicylic acid, 0-500 ng mL(-1) in serum and 0-300 ng mL(-1) in urine, and salicyluric acid, 0-300 ng mL(-1) in urine.

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